If you replace the fuel pump I would get the new turbin style pump and sender from Ford.
I will attach the TSB 97-23-9 below.
You might try a fuel filter first.
Disconnecting the battery will not cause it to run badly as it runs in open loop most of the time anyway.
I disconnect my engine battery every day on the road when I stop for the night. I also leave it disconnected while at home and charge it with it disconnected after two or more weeks of setting.
A good place to start would be to chack to see if you have any codes in stored Computer Memory (CM).
Also run a electrical test of all your engine sensors and solenoid with the KOEO self-test.
If you do not know how go to this link below:
http://fordfuelinjection.com/?p=13
Also put a fuel pressure gauge on it before saying the fuel pump is bad. Ground pin #6 of the self-test plug and turn on the key. You should get 40-45psi pressure on the gauge.